通解.... how do u do it??

Please see the deductions below:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Gensol.jpg

Note: The product to sum formula of sin A sin B should be:
sin Asin B = 0.5[cos (A-B) - cos (A+B)]
Hence sin 6xsin x = 0.5[cos (6x-x) - cos (x+6x)] = 0.5 (cos 5x - cos 7x) BUT NOT 0.5(cos 7x - cos 5x)

sin6xsinx=cos3xcos4x
0.5[cos7x-cos5x] = 0.5[cos7x+cosx]
cos7x-cos5x=cos7x+cosx
cosx+cos5x=0
2cos3xcos2x=0
cos3x = 0 or cos2x = 0
3x = 360n±90 or 2x = 360n±90 where n is a constant
x = 120n±30 or x=180n±45